Consider two copper wires with circular cross-sections and equal lengths. One wire has 3 times the diameter of the other. How do the resistances of these two wires compare?
A)The thicker wire has 1/3 the resistance of the thinner wire.
B)The thicker wire has 1/9 the resistance of the thinner wire.
C)The thicker wire has 3 times the resistance of the thinner wire.
D)The thicker wire has 9 times the resistance of the thinner wire.
E)The thicker wire has $\sqrt { 3 }$ times the resistance of the thinner wire.

Question

Quizplus · Accepted Answer

Resistance is inversely proportional to the cross-sectional area. If the diameter is tripled, the area increases by a factor of 9 (since area is proportional to the square of the diameter). Therefore, the resistance of the thicker wire is 1/9 that of the thinner wire.

Consider Two Copper Wires with Circular Cross-Sections and Equal Lengths 3\sqrt { 3 }3​

Consider Two Copper Wires with Circular Cross-Sections and Equal Lengths $\sqrt { 3 }$